Question

The cartesian equation of the line `overliner = (hati + hatj + hatk) + lambda(hatj + hatk)` is ______

Options

• x = 1, y = z

• `(x - 1)/1 = (y - 1)/2 = (z - 1)/2`

• x = y = z

• x - 1 = y = z

Answer 1

The cartesian equation of the line `overliner = (hati + hatj + hatk) + lambda(hatj + hatk)` is x = 1, y = z.

Explanation:

Putting `overliner = xhati + yhatj + zhatk` in the given equation,

`xhati + yhatj + zhatk = (hati + hatj + hatk) + lambda(hatj + hatk)`

∴ `xhati + yhatj + zhatk = hati + (1 + lambda)hatj + (1 + lambda)hatk`

∴ x = 1, y = 1 + λ, z = 1 + λ

∴ x = 1, y = z